We derived topological Hall effect for currents that pass adiabatically through magnetic materials that have continuous magnetizations directly from the Karplus Luttinger theory, and found an important implication that a Hall conductivity could deduce the polarity of a magnetic profile in the vortex state. This is a significant discovery as it may allow one to electrically detect binary information stored in the polarity of a magnetic vortex that is the natural ground state of a permalloy disc.